Laser apparatus

ABSTRACT

A laser apparatus capable of suppressing an influence of return light with respect to an optical output without causing an increase of a number of parts, an enlargement of the entire apparatus, or an increase of a power consumption, including a semiconductor laser having an optical resonator provided with a pair of opposing reflection mirrors, in which a resonator length is set to L in , constituted so as to obtain a constant optical output from the optical resonator under constant drive conditions, and set so that reflectivities R f  and R r  of the reflection mirrors absorb a change of an output light intensity due to a change of the phase of the return light.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a laser apparatus having anoptical resonator provided with a reflection portion such as asemiconductor laser.

[0003] 2. Description of the Related Art

[0004] A semiconductor laser for example has an optical resonatorconstituted by a pair of opposing reflection mirrors, that is, aFabry-Perot resonator.

[0005] It has been known that when a semiconductor laser having such astructure is built in an optical system with return light, the opticaloutput thereof changes along with a change of the phase of the returnlight (refer to for example Ryoichi Ito and Michiharu Nakamura ed.,Semiconductor Laser—Fundamentals and Applications—, Baifukan, 1989).

[0006] This fluctuation of the optical output becomes harmful noise invarious applications of semiconductor lasers.

[0007] For example, it becomes a cause of noise in the recording orreproduction signal in the case of recording or reproduction from anoptical disk, becomes a cause of noise in an optical signal in the caseof optical communication, and becomes a cause of uneven color density oruneven color in the case of a laser beam printer.

[0008] Therefore, in the related art, generation of noise has beensuppressed by installing an optical isolator, an optical shield plate,or a prism in the optical system so as to prevent the return light fromstriking the optical resonator of the semiconductor laser (refer to forexample Japanese Unexamined Patent Publication (Kokai) No. 61-151849,Japanese Unexamined Patent Publication (Kokai) No. 3-54730, and JapaneseUnexamined Patent Publication (Kokai) No. 6-162551), arranging anattenuation plate etc. for reducing the return light in comparison withthe output of the semiconductor laser (refer to for example JapaneseUnexamined Patent Publication (Kokai) No. 62-137734) and suppressing theinfluence of the return light, or superimposing a high frequency on adrive current particularly in the recording and reproduction from anoptical disk (refer to for example Japanese Unexamined PatentPublication (Kokai) No. 60-140551).

[0009] However, in these techniques of the related art mentioned above,there are the disadvantages that the number of parts becomes large, theentire apparatus becomes bigger, the assembly or adjustment thereof istroublesome, and the power consumption is increased.

SUMMARY OF THE INVENTION

[0010] The present invention was made in consideration with such acircumstance and has as an object thereof to provide a laser apparatuscapable of suppressing the influence of return light on the output lightwithout causing an increase of the number of parts, an enlargement ofthe entire apparatus, or an increase of the power consumption.

[0011] To attain the above object, according to a first aspect of thepresent invention, there is provided a laser apparatus having an opticalresonator provided with a reflection portion and obtaining a constantoptical output from the optical resonator under constant driveconditions, wherein a reflectivity of the reflection portion is set soas to absorb a change of an intensity of an output light due to a changeof a phase of return light.

[0012] Preferably, the laser apparatus is a current-driven semiconductorlaser, and the reflectivity of the reflection portion is set so thatthere is a predetermined optical output value in a region in whichcurrent-optical output characteristics expressing the optical outputwith respect to the drive current in different return light phasesintersect.

[0013] According to a second aspect of the present invention, there isprovided a laser apparatus having an optical resonator provided with apair of opposing reflection mirrors, obtaining a constant optical outputfrom said optical resonator under constant drive conditions, and usedbuilt-in an optical system in which part R_(ofb)P(0<R_(ofb)<1) of theoptical output P returns to the optical resonator as return light,wherein

[0014] when a time average value of the optical output P is defined asP_(av), where an absolute value |ΔP| of a fluctuation ΔP=P−P_(av) of theoptical output produced along with the change of a return light phase Ømust not be more than a constant proportion ε with respect to P_(av) andwhere |ΔP|/P_(av) must be not more than ε,

[0015] when the following are defined by designating a reflectivity ofthe side (forward) for fetching the optical output of the pair ofopposing reflection mirrors constituting said optical resonator asR_(f), the reflectivity of the side opposite to this (reverse) as R_(r),a resonator length as L_(in), an internal loss as α_(i), a differentialgain as g_(n), a proportion of coupling of the return light with thelight inside the laser as η_(t), the proportion of coupling of thereturn light with the output light from the laser as η_(r), and aninput/output efficiency and a threshold gain measured by a laserapparatus element where there is no return light as η_(s) ⁰ and g⁰,respectively, and using these parameters or physical constants:

Y ₁=1+{square root}{square root over (η_(r)R_(ofb)R_(f))}

Y ₂=1−{square root}{square root over (η_(r)R_(ofb)R_(f))}

[0016]$Z_{1} = {1 + {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{1}}}}$$Z_{2} = {1 - {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{2}}}}$$g_{1} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{1}}}$$g_{2} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{2}}}$$\quad {\frac{\eta_{S1}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{1} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{1}\left( {g^{0} - \alpha_{i}} \right)}{Y_{1}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{1}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{1}}} \right)}}$$\frac{\eta_{S2}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{2} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{2}\left( {g^{0} - \alpha_{i}} \right)}{Y_{2}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{2}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{2}}} \right)}$

[0017] the following stands:${2\varepsilon} \geq {{\left( {\frac{\eta_{S1}}{\eta_{S}^{0}} - \frac{\eta_{S2}}{\eta_{S}^{0}}} \right) + {\frac{\eta_{S}^{0}}{P_{av}g_{N}L_{in}\tau_{S}}\left\lbrack {{\frac{\eta_{s1}}{\eta_{S}^{0}}\ln \quad Z_{1}} - {\frac{\eta_{S2}}{\eta_{S}^{0}}\ln \quad Z_{2}}} \right\rbrack}}}$

[0018] According to a third aspect of the present invention, there isprovided a semiconductor laser apparatus having the optical resonatorprovided with a pair of opposing reflection mirrors, obtaining aconstant optical output from said optical resonator under constant driveconditions, and used built-in an optical system in which partR_(ofb)P(0<R_(ofb)<1) of the optical output P returns to the opticalresonator as return light, wherein

[0019] when a time average value of the optical output P is defined asP_(av), where an absolute value |ΔP| of the fluctuation ΔP=P−P_(av) ofthe optical output produced along with a change of a return light phaseØ must not be more than a constant proportion ε with respect to P_(av)and where |ΔP|/P_(av) must be not more than ε,

[0020] when the following are defined by designating a reflectivity ofthe side (forward) for fetching the optical output of the pair ofopposing reflection mirrors constituting said optical resonator asR_(f), a reflectivity of the side opposite to this (reverse) as R_(r),the resonator length as L_(in), the internal loss as α_(i), a volume ofan active region as V_(a), an optical confinement coefficient of theactive region as Γ, a proportion of an increase of the optical gain withrespect to an increase of a carrier density of the active region asg_(n), a carrier life of the carrier of the active region by spontaneousemission and a nonemission recoupling as τ_(s), a proportion of couplingof the return light with the light inside the laser as η_(t), aproportion of coupling of the return light with an output light from thelaser as η_(r), a slope efficiency and the threshold gain measured by alaser apparatus element where there is no return light as η_(S) ⁰ andg⁰, respectively, and an amount of charge as e, respectively, and usingthese parameters or physical constants:$Y_{1} = {1 + \sqrt{\eta_{r}R_{{ofb}\quad}R_{f}}}$$Y_{2} = {1 - \sqrt{\eta_{r}R_{ofb}R_{f}}}$$Z_{1} = {1 + {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{1}}}}$$Z_{2} = {1 - {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{2}}}}$$g_{1} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{1}}}$$g_{2} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{2}}}$$\quad {\frac{\eta_{S1}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{1} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{1}\left( {g^{0} - \alpha_{i}} \right)}{Y_{1}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{1}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z\quad {sub1}}} \right)}}$$\quad {\frac{\eta_{S1}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{1} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{2}\left( {g^{0} - \alpha_{i}} \right)}{Y_{2}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{2}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{2}}} \right)}}$

[0021] the following stands:${2\varepsilon} \geq {{\left( {\frac{\eta_{S1}}{\eta_{S}^{0}} - \frac{\eta_{S2}}{\eta_{S}^{0}}} \right) + {\frac{e\quad V\quad a\quad \eta_{S}^{0}}{P_{av}\Gamma \quad g_{N}L_{in}\tau_{S}}\left\lbrack {{\frac{\eta_{s1}}{\eta_{S}^{0}}\ln \quad Z_{1}} - {\frac{\eta_{S2}}{\eta_{S}^{0}}\ln \quad Z_{2}}} \right\rbrack}}}$

[0022] Preferably, when there is return light, it operates where thefluctuation in the optical output due to the return light in a specificoptical output is not more than a constant proportion (ε).

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The above object and features of the present invention will bemore apparent from the following description of the preferredembodiments given with reference to the accompanying drawings, wherein:

[0024]FIG. 1 is a schematic view when a semiconductor laser having aFabry-Perot resonator operates built into an optical system in whichthere is return light;

[0025]FIG. 2 is a view of a current-optical output characteristic of asemiconductor laser for explaining a state of change of a forwardoptical output P_(f) due to the change of a phase Ø of return light;

[0026]FIG. 3 is a view in which parameters are assigned in an equation,ε* is calculated by a computer by using reflectivity R_(f) and R_(r) offorward and reverse reflection mirrors as variables, and they areexpressed in the form of a contour; and

[0027]FIG. 4 is a view in which parameters of an AlGaAs semiconductor DHlaser wherein ε* becomes smaller than 0.05 are assigned in an equation,ε* is calculated by a computer by using the reflectivities R_(f) andR_(r) of the forward and reverse reflection mirrors as variables, andthey are expressed in the form of a contour.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0028] Below, embodiments of the laser apparatus according to thepresent invention will be explained in relation to the drawings.

[0029] In the embodiments, the explanation will be made by taking as anexample a case of a semiconductor laser having a Fabry-Perot resonatorconstituted by a pair of opposing reflection mirrors.

[0030]FIG. 1 is a schematic view in the case where a semiconductor laserhaving a Fabry-Perot resonator operates built into an optical system inwhich there is return light.

[0031] The semiconductor laser 10 according to the present invention hasa Fabry-Perot resonator 11 provided with a pair of opposing reflectionmirrors 11 f and 11 r and a resonator length set at L_(in), isconstituted so as to obtain a constant optical output from theFabry-Perot resonator 11 under constant drive conditions, and is set sothat the reflectivities Rf and Rr of the reflection mirrors 11 f and 11r absorb a change of the intensity of the output light due to a changeof the phase of the return light.

[0032] Note that the semiconductor laser 10 is for example constitutedby a laser of a double hetero (DH) structure (DH laser) comprised of anAlGaAs compound semiconductor in which a not illustrated clad layer ismade of Al_(y)Ga_((1−y))As and an active layer is made ofAl_(x)Ga_((1−x))As.

[0033] The semiconductor laser 10 is driven by a constant output (APCdrive) by feedback having a slower response than the speed of change ofthe phase Ø of the return light (return light phase) based on a DCcurrent drive (DC drive) or the optical phase inside the semiconductorlaser so as to obtain a constant optical output from the Fabry-Perotresonator 11 under constant drive conditions.

[0034] The reflectivities Rf and Rr of the reflection mirrors 11 f and11 r and various parameters are set as follows so as to absorb a changeof the intensity of the optical output due to the change of the returnlight.

[0035] Namely, the semiconductor laser 10 is constituted so that inapplications of the optical system in which it is built, when a timeaverage value of the optical output P is defined as P_(av), where anabsolute value |ΔP| of a fluctuation ΔP=P−P_(av) of the optical outputproduced along with the change of a return light phase Ø must not bemore than a constant proportion ε with respect to P_(av) that is,|ΔP|/P_(av) must be not more than ε, when the following are defined bydesignating a reflectivity of the side (forward) for fetching theoptical output of the pair of opposing reflection mirrors 11 f and 11 rconstituting the optical resonator 11 of the semiconductor laser 10 asR_(f), the reflectivity of the side opposite to this (reverse) as R_(r),a resonator length as L_(in), an internal loss as α_(i), a volume of anactive region as V_(a), an optical confinement coefficient of the activeregion as Γ, a proportion of an increase of the optical gain withrespect to an increase of a carrier density of the active region asg_(N), a carrier life of the carrier of the active region by spontaneousemission and a nonemission recoupling as τ_(S), a proportion of couplingof the return light with the light inside the laser as η_(t), aproportion of coupling of the return light with an output light from thelaser as η_(r), a slope efficiency and the threshold gain measured by alaser apparatus element where there is no return light as η_(s) ⁰ andg⁰, respectively, and an amount of charge as e, respectively, and usingthese parameters or physical constants:$Y_{1} = {1 + \sqrt{\eta_{r}R_{{ofb}\quad}R_{f}}}$$Y_{2} = {1 - \sqrt{\eta_{r}R_{ofb}R_{f}}}$$Z_{1} = {1 + {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{1}}}}$$Z_{2} = {1 - {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{2}}}}$$g_{1} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{1}}}$$g_{2} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{2}}}$$\quad {\frac{\eta_{S1}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{1} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{1}\left( {g^{0} - \alpha_{i}} \right)}{Y_{1}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{1}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}{Z\quad}_{1}}} \right)}}$$\quad {\frac{\eta_{S2}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{2} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{2}\left( {g^{0} - \alpha_{i}} \right)}{Y_{2}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{2}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{2}}} \right)}}$

[0036] the following stands:${2\varepsilon} \geq {{\left( {\frac{\eta_{S1}}{\eta_{S}^{0}} - \frac{\eta_{S2}}{\eta_{S}^{0}}} \right) + {\frac{e\quad V\quad a\quad \eta_{S}^{0}}{P_{av}\Gamma \quad g_{N}L_{in}\tau_{S}}\left\lbrack {{\frac{\eta_{s1}}{\eta_{S}^{0}}\ln \quad Z_{1}} - {\frac{\eta_{S2}}{\eta_{S}^{0}}\ln \quad Z_{2}}} \right\rbrack}}}$

[0037] Below, an explanation will be made, with reference to thedrawings, of the fact that a change of the intensity of the output lightdue to a change of the phase of the return light can be absorbed bysetting the reflectivities R_(f) and R_(r) of the reflection mirrors 11f and 11 r as mentioned above in the semiconductor laser 10.

[0038] Note that in the case of a distributed Bragg reflector (DBR)laser (DBR laser) where the reflection mirrors are replaced by gratingwaveguides, a similar discussion can be made by replacing thereflectivities relating to the optoelectric field amplitudes of thereflection mirrors or transmittance by a complex number.

[0039] Further, in the case of a vertical cavity surface emitting laser(VCSEL) as well, since the vertical resonator is constituted by a Braggreflector comprised of a dielectric or a semiconductor multi-layer film,the same discussion can be made as with a DBR laser.

[0040] Therefore, an explanation will be made later of the case of a DBRlaser containing a VCSEL.

[0041] First, consider FIG. 1, that is, a schematic view of the casewhere a semiconductor laser having a Fabry-Perot resonator operatesbuilt into an optical system having return light.

[0042] In FIG. 1, when the length of the resonator of the semiconductorlaser 10 is defined as L_(in), a z-axis is set so that the reversereflection mirror 11 r of the reflectivity R_(r) is located at z=−L_(in)and the forward reflection mirror 11 f of the reflectivity R_(f) islocated at z=0.

[0043] The light from the semiconductor laser is output from both ofthese two reflection mirrors 11 r and 11 f toward the outside.

[0044] At this time, the output from z=−L_(in) in a −z direction, thatis, in reverse, is defined as the reverse optical output P_(r), whilethe output from z=0 in a +z direction, that is, forward, is defined asthe forward optical output P_(f).

[0045] Between these optical outputs, the forward optical output P_(f)is used for the recording and reproduction from the optical disk andapplications in the optical communications etc. On the other hand, thereverse optical output P_(r) is frequently used for monitoring theoptical output of the semiconductor laser.

[0046] The forward optical output P_(f) from the semiconductor laser 10is partially reflected by the optical system to become return lightwhich is returned to the semiconductor laser.

[0047] Here, the position of generation of the most important returnlight from the optical system is expressed by an optically equivalentdistance L_(ex).

[0048] Further, the intensity of the return light is proportional to theforward light P_(f), therefore is expressed as P_(ofb)P_(f).

[0049] In FIG. 1, the optical system 20 generating this return light isequivalently expressed by an external mirror 21 having a reflectivityR_(ofb) placed at the position of z=L_(ex).

[0050] In the return light R_(ofb)P_(f) returned to the semiconductorlaser 10, part R_(f)R_(ofb)P_(f) thereof is reflected by the forwardreflection mirror 11 f, and part having a proportion of 0<η_(r)≦1 in thereflected light is coupled with the forward output light P_(f) from thesemiconductor laser.

[0051] Further, in the return light R_(ofb)P_(f) returned to thesemiconductor laser 10, a part having a proportion of 0<η_(t)≦1 in thelight (1−R_(f)) R_(ofb)P_(f) not reflected by the forward reflectionmirror 11 f, but transmitted through the forward reflection mirror 11 fis coupled with the light advanced in the −z direction inside thesemiconductor laser.

[0052] By the coupling of the return light with the light inside thesemiconductor laser or the emitted light from the semiconductor laser,the forward optical output P_(f) becomes a value different from that ofthe optical output when there is no return light.

[0053] Further, it has been also known that, according to some intensityand phase of the return light or distance L_(ex) up to the return lightgeneration position, the operating state of the semiconductor laser 10changes due to the influence of the return light and that a phenomenonwhere the optical output periodically or chaotically vibrates in a bandof a frequency determined by L_(ex), i.e., f_(ex)≡c/2L_(ex)© is thespeed of light in vacuum).

[0054] Such an optical output vibration sometimes becomes a problem inapplication. In this case, there is no method for solving the problemother than the method of reducing the intensity of the return light perse as much as possible.

[0055] However, when the frequency band important in the application islower than the frequency band of the optical output vibrationrepresented by f_(ex), a fluctuation of an average optical outputobtained by averaging these optical output vibrations at a time intervalof for example T>1/f_(ex) becomes a problem.

[0056] It can be confirmed from experiments or numerical calculationsthat the value of this time averaged optical outputs is substantiallyequal to the value assuming the steady state.

[0057] Therefore, it is possible to assume a steady state as follows tofind the equation of the forward optical output P_(f) when there is thereturn light and reduce the fluctuation of the forward optical outputP_(f) due to the return light in the frequency region lower than f_(ex)to such an extent where there is no problem in the application based onthis.

[0058] A complex amplitude of the intensity of the electric field of thelight just near the forward reflection mirror inside the semiconductorlaser, that is, at z=−0 and advancing in the −z direction, is expressedby E, the complex amplitude of the intensity of the electric field ofthe light emitted forward from the semiconductor laser just near theforward reflection mirror, that is at z=+0, is expressed as E_(f), andthe complex amplitude of the intensity of the electric field of thelight emitted reverse from the semiconductor laser just near the reversereflection mirror, that is, at z=−L_(in)+0, is expressed as E_(r).

[0059] The complex amplitudes E_(f) and E_(r) of the intensity of theelectric field have the following relationships with the forward opticaloutput P_(f) and the reverse optical output P_(r), respectively:

P _(f) =cε ₀ |E _(f)|²   (1)

P _(r) =cε ₀ |E _(r)|²   (2)

[0060] Here, ε₀ is the dielectric constant of vacuum, and c is the speedof light in vacuum.

[0061] The internal optical loss determined by the semiconductormaterial constituting the semiconductor laser 10 and the structure ofthe semiconductor laser is defined as α_(i), the gain produced byexcitation of the optical active region of the semiconductor laser dueto the injection of the current is defined as g, and the equivalentrefractive index of the resonator determined by the materialconstituting the semiconductor laser and the structure of thesemiconductor laser is defined as n.

[0062] There is no problem even if the internal optical loss α_(i) andthe gain g are assumed to be spatially uniform in the resonator of thesemiconductor laser 10.

[0063] As already explained, it is assumed that oscillation occurs inthe steady state and the oscillation wavelength thereof in the vacuum isdefined as λ.

[0064] At this time, the following relations stand among E, E_(f), andE_(r): $\begin{matrix}{{E_{f}/\sqrt{n}} = {{\sqrt{\left( {1 - R_{f}} \right)R_{r}}{\exp \left\lbrack {{\left( {g - \alpha_{i}} \right)L_{in}} - \frac{4\quad \pi \quad i\quad n\quad L_{in}}{\lambda}} \right\rbrack}E} - \quad {\sqrt{\eta_{r}R_{f}R_{ofb}}{\exp \left( \frac{{- 4}\quad \pi \quad i\quad L}{\lambda} \right)}{E_{f}/\sqrt{n}}}}} & (3) \\{E = {{\sqrt{R_{f}R_{r}}{\exp \left\lbrack {{\left( {g - \alpha_{i}} \right)L_{in}} - \frac{4\pi \quad i\quad {nL}_{in}}{\lambda}} \right\rbrack}E} + \quad {\sqrt{{\eta_{t}\left( {1 - R_{f}} \right)}R_{ofb}}{\exp \left( \frac{{- 4}\pi \quad i\quad L_{ex}}{\lambda} \right)}{E_{f}/\sqrt{n}}}}} & (4) \\{{E_{r}/\sqrt{n}} = {\sqrt{1 - R_{r}}{\exp \left\lbrack {\frac{\left( {g - \alpha_{i}} \right)L\quad i\quad n}{2} - \frac{2\pi \quad i\quad n\quad L_{in}}{\lambda}} \right\rbrack}E}} & (5)\end{matrix}$

[0065] Here, a steady oscillation state is assumed, so E and E_(f) arenot zero.

[0066] Therefore, the next equations which should be satisfied by thegain g and the oscillation wavelength λ are obtained from equations (3)and (4) after eliminating E and E_(f). $\begin{matrix}{g = {\alpha_{i} + {\frac{1}{2L_{in}}\ln \quad \frac{1}{R_{f}R_{r}}} - {\frac{1}{L_{in}}{l\left( {Z} \right)}}}} & (6) \\{p = {\frac{2{nL}_{in}}{\lambda} - {\frac{1}{2\pi}{{Arg}(Z)}\quad \left( {p:{integer}} \right)}}} & (7)\end{matrix}$

[0067] Here, Arg{Z} expresses an argument of the complex number Z, and Zis defined as follows: $\begin{matrix}{Z \equiv {1 + {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\left( {1 - R_{f}} \right)\frac{\exp \left( {{- i}\quad \varnothing} \right)}{Y}}}} & (8)\end{matrix}$

Y≡1+{square root}{square root over (η_(r)R_(f)R_(ofb))} exp(−iØ)   (9)

[0068] Here, the phase Ø≡4ΠL_(ex)/λ of the return light based on theoptical phase inside the laser was defined.

[0069] On the other hand, rate equations describing the operation of thesemiconductor laser are assumed as follows with respect to the number ofphotons S inside the optical resonator 11 of the semiconductor laser 10and the carrier density N of the active region: $\begin{matrix}{\frac{S}{t} = {{\frac{c}{n}\left\lbrack {{\Gamma \quad {G(N)}} - g} \right\rbrack}S}} & (10) \\{\frac{N}{t} = {\frac{I}{e\quad V_{a}} - \frac{N}{\tau_{S}} - {\frac{c}{n}\Gamma \quad {G(N)}\quad \frac{S}{V_{a}}}}} & (11)\end{matrix}$

[0070] Here, the optical gain generated in the active region due to theinjected carriers is expressed by a function G(N) of the carrier densityN. Further, the contribution of the spontaneously emitted light withrespect to the change of the number of photons along with time is notimportant so is ignored in the following discussion.

[0071] Further, as mentioned above, e is the amount of the charge, I isthe injected current, Γ is the optical confinement coefficientdetermined by the structure of the semiconductor laser, V_(a) is thevolume of the active region determined by the structure of thesemiconductor laser, and τ_(s) is the carrier life determined by theprobability of spontaneous emission and the probability of nonemissionrecoupling determined by the material and structure.

[0072] In the rate equations (10) and (11), if S of the steadyoscillation state is found by defining S>0, dS/dt=0, and dN/dt=0, thefollowing equation is obtained: $\begin{matrix}{S = {\frac{n}{ceg}\left( {I - I_{th}} \right)}} & (12)\end{matrix}$

[0073] Here, the threshold current value I_(th) is defined as in thefollowing equation by using an inverse function G⁻¹ of the optical gainG(N): $\begin{matrix}{I_{th} \equiv {\frac{{eV}_{a}}{\tau_{S}}{G^{- 1}\left( {g/\Gamma} \right)}}} & (13)\end{matrix}$

[0074] Since S>0, equation (12) has a meaning only when the injectedcurrent I is larger than the threshold current value I_(th), that is,I>I_(th). When I≦I_(th), the contribution of the spontaneously emittedlight is ignored here, so S=0.

[0075] In the rate equation used here, it is assumed that the currentinjected into the semiconductor laser is all consumed in the activeregion.

[0076] However, in actuality, there are a current flowing in a regionother than the active region and a current which flows in the activeregion but is not consumed and leaves.

[0077] In order to incorporate the contribution of these invalidcurrents in the equation of S, two parameters 0<ζ≦1 and ΔI_(th)≧0 areintroduced, and equation (12) is rewritten as follows: $\begin{matrix}{S \equiv {\frac{\zeta \quad n}{ceg}\left( {I - I_{th} - {\Delta \quad I_{th}}} \right)}} & (14)\end{matrix}$

[0078] That is, ΔI_(th) expresses the increase of the threshold currentdue to the invalid current, and ζ expresses the fact that the proportionof the increase of the number of photons when the current is increasedbecomes small in comparison with the case of the original equation (12)since there is the invalid current.

[0079] Next, the relationship between the number of photons S inside theresonator of the semiconductor laser and the electric field intensity Ewill be found.

[0080] The dependency of the electric field intensity inside the opticalresonator 11 of the semiconductor laser 10 with respect to the time tand the position z is expressed as E⁺(z)exp[i(ωt−kz)]+E⁻(z)exp[i(ωt+kz)]by the light exp[i(ωt+kz)] advancing in the ±z direction and the complexamplitude E±(z) depending upon each z.

[0081] Here, ω=2Πc/λ is an angle frequency of the laser beam, andk=2Πn/λ is a wave number inside the semiconductor laser resonator of thelaser beam.

[0082] The electric field intensity E is defined as the amplitude of thetraveling wave in the reverse direction, therefore a relationship ofE⁻(z=0)=E stands.

[0083] The gain g and the internal loss α_(i) are assumed to bespatially uniform, so become as follows when −L_(in)≦z≦0:$\begin{matrix}{{E^{-}(z)} = {E\quad {\exp \left( {{- \frac{g - \alpha_{i}}{2}}z} \right)}}} & (15) \\{{E^{+}(z)} = {\sqrt{R_{r}}E\quad e^{{- 2}{ikLin}}{\exp \left\lbrack {\frac{g - \alpha_{i}}{2}\left( {{2L_{in}} + z} \right)} \right\rbrack}}} & (16)\end{matrix}$

[0084] Using these equations, the number of photons S inside the opticalresonator 11 of the semiconductor laser 10 is expressed by |E|² asfollows: $\begin{matrix}{S = {{\frac{n^{2}\varepsilon_{0}}{\hslash \quad \omega}{\int_{- {Lin}}^{o}{{z\left( {{{E^{+}(z)}}^{2} + {{E^{-}(z)}}^{2}} \right)}}}}\quad = {\frac{n^{2}\varepsilon_{0}}{{\hslash \quad \omega}\quad}\frac{{E}^{2}}{g - \alpha_{i}}\left( {e^{{({g - {\alpha \quad i}})}{Lin}} - 1} \right)\left( {1 + {R_{r}e^{{({g - {\alpha \quad i}})}{Lin}}}} \right)}}} & (17)\end{matrix}$

[0085] Here, {overscore (h)} is the constant obtained by dividingPlanck's constant h by 2Π, and {overscore (h)}ω is the energy perphoton.

[0086] When equation (6) of the gain g is substituted into thisequation, the relationship between the number of photons S and theelectric field intensity E as shown in the following equation isobtained: $\begin{matrix}{S = {\frac{n^{2}\varepsilon_{0}}{\hslash \quad {\omega \left( {g - \alpha_{i}} \right)}}\left( {{\sqrt{\frac{R_{r}}{R_{f}}}\frac{1}{Z}} + 1} \right)\left( {{\sqrt{\frac{1}{R_{f}R_{r}}}\frac{1}{Z}} - 1} \right){E}^{2}}} & (18)\end{matrix}$

[0087] Taking note of condition equations (6) and (7) satisfied by thegain g and the oscillation wavelength λ, by eliminating E_(f) fromequations (1) and (4), further eliminating |E|² using equation (18), andfurther eliminating S by using equation (14), the equation of theforward optical output P_(f) is obtained as follows:

P _(f) =ηs(I−Ith−ΔIth)   (19)

[0088] Here, the slope efficiency η_(s) was defined by the followingequation: $\begin{matrix}{\eta_{s} \equiv {\frac{{\zeta\hslash}\quad \omega}{e}\frac{g - {\alpha \quad i}}{g}\frac{\left( {1 - R_{f}} \right)}{{Y}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}{Z}}} \right)\left( {1 + {\sqrt{R_{f}/R_{r}}{Z}}} \right)}}} & (20)\end{matrix}$

[0089] The forward optical output P_(f) depends upon the return lightphase Ø=4ΠL_(ex)/λ through Y and Z contained in equations (13), (20),and (6) of the threshold current value I_(th), slope efficiency η_(s),and gain g.

[0090] For example, if the position of occurrence of the return lightfrom the optical system changes even in a very small amount of about thewavelength λ, the return light phase Ø changes by 2Π or more through thechange of the position L_(ex) of generation of the return light.

[0091] Further, in the optical system into which the actualsemiconductor laser is built, the position (distance) L_(ex) of thegeneration of the return light is larger than the oscillation wavelengthλ in many cases.

[0092] Accordingly, even in a case where the temperature of thesemiconductor laser element changes due to a heat generation or the likeand the oscillation wavelength thereof slightly changes, the returnlight phase Ø largely changes.

[0093] For example, where a semiconductor laser having an oscillationwavelength of λ=1 μm is used in an optical system in which the positionof generation of the return light is L_(ex)=1 cm, the return light phaseØ changes by about 4Π even by a change of the oscillation wavelength byonly 0.01%. In many cases, a change of the temperature of thesemiconductor laser element of 1° C. is sufficient for occurrence of achange of 0.01% of this oscillation wavelength λ.

[0094] It is seen from equations (9) and (8) that |Y| and |Z| changefrom maximum values to minimum values when such a change of the returnlight phase Ø occurs.

[0095] Along with this, according to equation (19), the optical outputP_(f) of the semiconductor laser operating by the constant injectedcurrent I changes.

[0096] That is, if the injected current I is constant or even in a casewhere the optical output P_(f) or P_(r) is monitored and the injectedcurrent I is controlled by the feedback so as to hold this at a constantvalue, if it can be regarded that the response speed of the feedbackcontrol is slower than the speed of change of the return light phase Øand the injected current I is constant with respect to the change of thereturn light phase Ø, it can be theoretically derived that the forwardoptical output P_(f) changes due to a slight change of the positionL_(ex) of the generation of the return light or the change of the returnlight phase Ø due to the change of the oscillation wavelength λ of thesemiconductor laser.

[0097] Note that, at this time, simultaneously, it is possible toindicate that the reverse optical output P_(r) changes as well, but theexplanation thereof is omitted here.

[0098] The situation of the change of the forward optical output P_(f)due to the change of this return light phase Ø will be explained indetail based on FIG. 2 showing the current-optical output characteristicof the semiconductor laser.

[0099] Note that, in FIG. 2, the abscissa indicates the operating(injected) current value I, and the ordinate indicates the forwardoptical output P_(f).

[0100] When the current I is increased from 0, if I exceeds thethreshold current value I_(th)+ΔI_(th), the forward optical output P_(f)is abruptly increased and the semiconductor laser oscillates.

[0101] The proportion of the increase of the forward optical outputP_(f) with respect to the current I in this oscillation state, that is,the inclination of the current-optical output characteristic, is theslope efficiency η_(S).

[0102] The threshold current value Ith and the slope efficiency η_(S)change due to the change of the return light phase Ø as alreadyexplained.

[0103] In FIG. 2, the situation of the change is exaggeratedly drawn foreasier understanding. It does not show the characteristic of an actualsemiconductor laser. At this time, when the threshold current I_(th) isincreased due to the change of the return light phase Ø, the slopeefficiency η_(S) is also increased. When the threshold current valueI_(th) is reduced, the slope efficiency η_(S) is also reduced.

[0104] Accordingly, as shown in FIG. 2, there is a narrow region X inwhich the current-optical output characteristics at different returnlight phases Ø intersect with each other.

[0105] In this region X, when the operating current value I is constant,the change of the forward optical output P_(f) is small even if thereturn light phase Ø changes. On the other hand, in regions other thanthe region X, where the operating current value I is constant, theforward optical output P_(f) changes by a large extent if the returnlight phase Ø changes.

[0106] The semiconductor laser 10 according to the present embodiment issuitably designed and fabricated so that there is a predeterminedoptical output value in this region X in which current-optical outputcharacteristics having different return light phases Ø intersect.

[0107] Below, by utilizing equation (19), a condition necessary fordesign and configuration of the laser apparatus in which the fluctuationΔP of the optical output from P_(av) is placed in the range of apredetermined proportion with respect to the forward optical outputP_(av) obtained by averaging over time at a sufficiently long timeinterval in comparison with the speed of the change of the return lightphase even if the return light phase Ø changes is found.

[0108] It is learned that when the return light phase Ø fluctuates, theforward optical output P_(av) averaged in time takes a value near theforward optical output P_(f) where there is no return light.

[0109] Further, a magnitude ΔP of the fluctuation of the forward opticaloutput P_(f) accompanying the fluctuation of the return light phase Øbecomes at the most half of a difference between the value of theforward optical output P_(f) when Ø is set equal to 0 and the value ofthe forward optical output P_(f) when Ø is set to equal to Π in equation(19) except in the region X shown in FIG. 2,

[0110] These facts are expressed by equations as follows:

P _(av)=η_(S) ⁰(I−I _(th) ⁰ −ΔI _(th))   (21)

|ΔP|≦|η _(S)(Ø=0)(I−I _(th)(Ø=0)−ΔI _(th))−η_(S)(Ø=π)(I−I _(th)(Ø=π)−ΔI_(th))|/2   (22)

[0111] Here, η_(S) ⁰ and I_(th) ⁰ express values of the slope efficiencyη_(S) and the threshold current I_(th) in the case where there is noreturn light, that is. R_(ofb)=0, respectively.

[0112] In the region X, equation (22) does not stand, but if it isdesigned so that the magnitude ΔP of the fluctuation becomes ε or lessbased on this equation, the predetermined forward optical output valuecan be made exist in the region X or in the vicinity of the region X.

[0113] When eliminating the injected current value I from equation (22)by using equation (21) and further dividing both sides by P_(av), thefollowing equations are obtained: $\begin{matrix}{\frac{{\Delta \quad P}}{P_{av}} \leq {\frac{1}{2}{\begin{matrix}{{\frac{\eta_{s}(0)}{\eta_{S}^{0}}\left\{ {1 - {\frac{\eta_{S}^{0}}{P_{av}}\left\lbrack {{I_{th}(0)} - I_{th}^{0}} \right\rbrack}} \right\}} -} \\{\frac{\eta_{S}(\pi)}{\eta_{S}^{0}}\left\{ {1 - {\frac{\eta_{S}^{0}}{P_{av}}\left\lbrack {{I_{th}(\pi)} - I_{th}^{0}} \right\rbrack}} \right\}}\end{matrix}}}} & (23)\end{matrix}$

[0114] When the right side of this inequality is made ε*, ε* can becontrolled to the target value of ε or less by suitably designing thesemiconductor laser using P_(av) as the target optical output of thesemiconductor laser.

[0115] That is, when ε* is set as in the following equation, asemiconductor laser is obtained in which the absolute value |ΔP| of theoptical output fluctuation is a constant proportion ε or less withrespect to the average optical output P_(av), that is, |ΔP|/P_(av)≦ε*≦ε.$\begin{matrix}{\varepsilon^{*} \equiv {\frac{1}{2}{\begin{matrix}{{\frac{\eta_{s}(0)}{\eta_{S}^{0}}\left\{ {1 - {\frac{\eta_{S}^{0}}{P_{av}}\left\lbrack {{I_{th}(0)} - I_{th}^{0}} \right\rbrack}} \right\}} -} \\{\frac{\eta_{S}(\pi)}{\eta_{S}^{0}}\left\{ {1 - {\frac{\eta_{S}^{0}}{P_{av}}\left\lbrack {{I_{th}(\pi)} - I_{th}^{0}} \right\rbrack}} \right\}}\end{matrix}}}} & (24)\end{matrix}$

[0116] In order to actually design and fabricate a semiconductor laser,it would be convenient if there were a simpler equation of ε*. Below, anapproximate equation of such an ε* is derived.

[0117] First, I_(th)(0)−I_(th) ⁰ and I_(th)(Π)−I_(th) ⁰ contained inequation (24) are simplified by using approximation. If equation (13) ofthe threshold current value I_(th) is used, it can be expressed as inthe following equation: $\begin{matrix}{{{I_{th}(\varnothing)} - I_{th}^{0}} = {\frac{e\quad V_{a}}{\tau_{S}}\left\lbrack {{G^{- 1}\left( {g/\Gamma} \right)} - {G^{- 1}\left( {g^{0}/\Gamma} \right)}} \right\rbrack}} & (25)\end{matrix}$

[0118] Here, g⁰≡α_(i)−1n (R_(f)R_(r))/(2L_(in)) is the gain g when thereis no return light.

[0119] The dependency G(N) of the optical gain generated in the activeregion with respect to the carrier density N is approximated by a linearfunction in the vicinity of the carrier density at which thesemiconductor laser operates thereby to obtain G(N)=g_(N)(N−N_(t)).

[0120] Here, g_(N) and N_(t) are coefficient parameters at the time ofapproximation. In particular, g_(N) is the parameter expressing how muchthe optical gain increases with respect to an increase of the carrierdensity in the vicinity of the carrier density at which thesemiconductor laser operates—important when fabricating a semiconductorlaser.

[0121] When using this approximation, equation (25) can be modified asfollows by using equation (6) satisfied by the gain g: $\begin{matrix}{{{I_{th}(\varnothing)} - I_{th}^{0}} = {{\frac{e\quad V_{a}}{\tau_{S}}\left( {\frac{g}{\Gamma \quad g_{N}} - \frac{g^{0}}{\Gamma \quad g_{N}}} \right)} = {{- \frac{e\quad V_{a}}{\Gamma \quad g_{N}L_{in}\tau_{S}}}{\ln \left( {{Z(\varnothing)}} \right)}}}} & (26)\end{matrix}$

[0122] From this equation, I_(th)(0)−I_(th) ⁰ and I_(th)(Π)−I_(th) ⁰ canbe simply expressed as in the following equations, respectively:$\begin{matrix}{{{I_{th}(0)} - I_{th}^{0}} = {{- \frac{e\quad V_{a}}{\Gamma \quad g_{N}L_{in}\tau_{S}}}\ln \quad {Z(0)}}} & (27) \\{{{I_{th}(\pi)} - I_{th}^{0}} = {{- \frac{e\quad V_{a}}{\Gamma \quad g_{N}L_{in}\tau_{S}}}\ln \quad {Z(\pi)}}} & (28)\end{matrix}$

[0123] In these modified equations, the fact that Y(0), Y(Π), Z(0), andZ(Π) are real numbers was used.

[0124] By using equations (27) and (28), equation (24) of ε* can berewritten to the following simple format: $\begin{matrix}{\varepsilon^{*} = {\frac{1}{2}{{\left\lbrack {\frac{\eta_{s}(0)}{\eta_{S}^{0}} - \frac{\eta_{S}^{0}(\pi)}{\eta_{S}^{0}}} \right\rbrack + \quad {\frac{1}{P_{av}}{\frac{e\quad V_{a}\eta_{S}^{0}}{\Gamma \quad g_{N}L_{in}\tau_{S}}\left\lbrack {{\frac{\eta_{S}(0)}{\eta_{S}^{0}}\quad \ln \quad {Z(0)}} - {\frac{\eta_{S}(\pi)}{\eta_{S}^{0}}\ln \quad {Z(\pi)}}} \right\rbrack}}}}}} & (29)\end{matrix}$

[0125] Here, by equation (20) of the slope efficiency η_(S),η_(S)(Ø)/η_(S) ⁰ (Ø=0 or Π) is expressed as follows when noting thatY(0), Y(Π), Z(0), and Z(Π) are still real numbers: $\begin{matrix}{{\frac{\eta_{S}(\varnothing)}{\eta_{S}^{0}} = \left\lbrack \frac{g^{0}\left( {{g(\varnothing)} - \alpha_{i}} \right)}{{g(\varnothing)}\left( {g^{0} - \alpha_{i}} \right)} \right\rbrack}{x\quad \frac{\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{Y^{2}(\varnothing)}\left( {1 - {\sqrt{R_{f}R_{r}}{Z(\varnothing)}}} \right)\left( {1 + {\sqrt{R_{f}/R_{r}}{Z(\varnothing)}}} \right)}\quad \left( {\varnothing = {0\quad {or}\quad \pi}} \right)}} & (30)\end{matrix}$

[0126] When defining Y₁≡Y(0), Y₂≡Y(Π), Z₁≡Z(0), Z₂≡Z(Π), g₁≡g(0),g₂≡g(Π), η_(S1)≡η_(S)(0), and η_(S2)≡η_(S)(Π), from equation (29), theinequality ε*≦ε is equivalent to the condition equations indicated byequations (1) and (2).

[0127] Below, based on equation (29), an example of the method ofproduction of a semiconductor laser realizing the targeted ε* at thepredetermined time averaged optical output P_(av) will be explained.

[0128] An apparatus constituted by a laser of a double hetero (DH)structure (DH laser) comprised of a general AlGaAs compoundsemiconductor and in which the clad layer is made of Al_(y)Ga_((1−Y))Asand the active layer is made of Al_(x)Ga_((1−x))As, with a return lightof 1%, that is, R_(ofb)=0.01, and with a maximum value of the opticaloutput fluctuation due to the return light of ε=0.05 or less, that is,5% or less, when the time average forward output P_(av) is 5 mW whenbuilt in an optical system in which the coupling efficiency of thereturn light is expressed by η_(r)η_(t)=1 is for example designed asfollows:

[0129] The Al composition x of the active layer is determined by theoscillation wavelength λ and is selected to be about x=0.12 in the casewhere λ=0.78 μm. The Al composition y of the clad layer is selected tobe x<y so that the carriers and the light are sufficiently confined inthe active region and is selected as for example y=0.47.

[0130] The internal loss α_(i) and the carrier life τ_(s) are mainlydetermined by the material. In the case of an AlGaAs compoundsemiconductor, α_(i)=10 cm⁻¹ and π_(s)=2 ns are respectivelyrepresentative values.

[0131] When defining the length of the resonator of the semiconductorlaser as L_(in)=250 μm, the thickness of the Al_(x)Ga_((1−x))As activelayer as 0.1 μm, and the width of the region into which the current isinjected and which optically becomes active as 3 μm, the volume of theactive region becomes V_(a)=75 μm³, and the optical confinementcoefficient becomes about Γ=0.1.

[0132] The proportion g_(N) of the increase of the optical gain withrespect to the increase of the carrier density and the parameter ζexpressing the effect of the invalid current are determined by thematerial and the structure. These are estimated as being aboutg_(N)=7×10⁻¹⁶ cm⁻¹⁶/cm⁻³ and ζ=0.9 in the case of the above material andstructure.

[0133]FIG. 3 is a contour view obtained by substituting the aboveparameters into equation (24), calculating the ε* by a computer by usingthe remaining design parameters of the semiconductor laser, that is, thereflectivities R_(f) and R_(r) of the forward and reverse reflectionmirrors as variables, and expressing the result thereof in the form of acontour.

[0134] In FIG. 3, by selecting the reflectivities R_(f) and R_(r) in thehatched region surrounded by the two broken lines indicated by ε*=0.05to fabricate the semiconductor laser, the target laser of ε*≦ε=0.05 canbe obtained.

[0135] Due to the variations at the fabrication of the semiconductorlaser, when taking into account the fact that values of parameters ofthe actually completed laser deviate from the designed values, desirablyR_(f) and R_(r) of the designed values are selected on a line indicatedby ε*=0 in FIG. 3.

[0136] However, in order to make the characteristics of thesemiconductor laser other than the amount of fluctuation of the opticaloutput due to the return light, for example, the threshold current valueI_(th) and the slope efficiency η_(s), the desired values, theysometimes cannot always be selected on the line of ε*=0. Also in thiscase, desirably they should be as close to the line of ε*=0 as possible.

[0137] By using a similar method to that described above, in the case ofP_(av)=30 mW, the AlGaAs semiconductor DH laser in which ε* becomessmaller than 0.05 can be obtained by selecting the forward and reversereflectivities R_(f) and R_(r) in the hatched region surrounded by thetwo broken lines of ε*=0.05 shown in FIG. 4 when the rest of thestructure is made the same as that described above. Also in this case,designed values near the line of ε*=0 as much as possible are selected.

[0138] In these examples, by using R_(f) and R_(r) as finally remainingparameters, these values were determined so that ε* becomes thepredetermined value. The reason why they were finally determined is thatthey can be freely easily determined in comparison with other parametersat the stage of design and fabrication of a semiconductor laser.

[0139] However, of course, it is also possible to perform the design soas to obtain a desired value of ε* by adjusting other parameters.

[0140] For example, adjustment of the volume V_(a) of the active regionand the resonator length L_(in) is relatively easy in the design orfabrication of a laser.

[0141] Further, by adopting a structure other than a DH structure, forexample, a quantum well structure or a SCH structure, as the structureof the active region, the proportion g_(N) of the increase of the gainwith respect to the carrier density and the optical confinementcoefficient Γ can be adjusted to a certain extent.

[0142] Further, while the above examples concerned a semiconductor laserusing a AlGaAs semiconductor as a material, as immediately understoodfrom the above explanation, even in the case where another semiconductormaterial is used, by designing and fabricating this based on equation(29) by using parameters expressing the characteristics of the material,it is possible to make ΔP the predetermined proportion ε or less inP_(av).

[0143] The explanation heretofore was made concerning a semiconductorlaser having a Fabry-Perot resonator (hereinafter referred to as an FPlaser), but in the case of a distributed Bragg reflector laser as well(hereinafter referred to as a DBR laser) replacing the reflectionmirrors by grating waveguides, as shown below, by replacing thereflectivity and transmission rate for the opto-electric field amplitudeof the reflection mirrors by the reflectivity and transmittance of thegrating waveguides expressed by complex numbers, a laser apparatus inwhich the proportion of the optical output fluctuation ΔP with respectto the average output P_(av) is placed in ε or less even if there is achange of the return light phase Ø can be similarly constituted.

[0144] Further, in a vertical cavity surface emitting laser (VCSEL)using a vertical resonator as well, the reflection mirrors constitutingthe optical resonator can be considered equivalent to a DBR laser sinceit is a Bragg reflection unit comprising a multi-layer film made ofsemiconductor or a dielectric.

[0145] The reflectivity of the grating waveguide replacing the forwardreflection mirror with respect to the electric field amplitude of thelight is defined as (R_(f)){fraction (1/2)}exp(iψ₁) with respect to thelight incident from the −z direction and is defined as (R_(f)){fraction(1/2)}₂) with respect to the light incident from the +z direction. Thetransmittance of this grating waveguide with respect to the electricfield amplitude of the light is defined as (T_(f)){fraction(1/2)}exp(iψ₃).

[0146] Further, the reflectivity of the grating waveguide replacing thereverse reflection mirror with respect to the electric field amplitudeof the light incident from the +z direction is defined as(R_(r)){fraction (1/2)}exp(iψ₄), and the transmittance of this gratingwaveguide with respect to the electric field amplitude is defined as(T_(r)){fraction (1/2)}exp(iψ₅) .

[0147] When the relations (3), (4), and (5) standing among E, E_(f), andE_(r) are rewritten by using these amounts, the following equations areobtained: $\begin{matrix}\begin{matrix}{{\left. {{E_{f}/\sqrt{n}} = \quad {{\sqrt{T_{f}r_{r}}{\exp \left\lbrack \left( {g - a_{i}} \right) \right\rbrack}L_{in}} - \frac{4\pi \quad i\quad n\quad L_{in}}{\lambda} + {\quad \psi_{3}} + {\quad \psi_{4}}}} \right\rbrack E} -} \\{\quad {\sqrt{\eta_{r}R_{f}R_{ofb}}{\exp \left( {{\quad \psi_{2}} - \frac{4\quad \pi \quad i\quad L_{in}}{\lambda}} \right)}{E_{f}/\sqrt{n}}}}\end{matrix} & (31) \\\begin{matrix}{E = \quad {{\sqrt{R_{f}R_{r}}{\exp \left\lbrack {{\left( {g - \alpha_{i}} \right)L_{in}} - \frac{4\pi \quad i\quad n\quad L_{in}}{\lambda} + {\quad \psi_{1}} + {\quad \psi_{4}}} \right\rbrack}E} +}} \\{\quad {\sqrt{\eta_{t}T_{f}R_{ofb}}{\exp \left( {{\quad \psi_{3}} - \frac{4\pi \quad i\quad L_{ex}}{\lambda}} \right)}{E_{f}/\sqrt{n}}}}\end{matrix} & (32) \\{{E_{f}/\sqrt{n}} = {\sqrt{T_{r}}{\exp \left\lbrack {\frac{\left( {g - \alpha_{i}} \right)L_{in}}{2} - \frac{2\quad \pi \quad i\quad n\quad L_{in}}{\lambda} + {\quad \psi_{5}}} \right\rbrack}E}} & (33)\end{matrix}$

[0148] When repeating analysis similar to the previous one by usingthese relations, it is understood that the equation of the forwardoptical output P_(f) of the FP laser stands also with respect to the DBRlaser as it is if the equations of Y and Z are rewritten as follows:$\begin{matrix}{\hat{Z} \equiv {^{{({{\psi 1} + {\psi \quad 4}})}}\left\lbrack {1 + {\sqrt{\frac{n_{t}R_{ofb}}{R_{f}}}\frac{T_{f}{\exp \left\lbrack {\left( {{- \varnothing} + {2\psi_{3}} - \psi_{1}} \right)} \right\rbrack}}{\hat{Y}}}} \right\rbrack}} & (34) \\{\hat{Y} \equiv {1 + {\sqrt{n_{r}R_{f}R_{ofb}}{\exp\left\lbrack {\left( {{- \varnothing} + \psi_{2}} \right\rbrack} \right.}}}} & (35)\end{matrix}$

[0149] The coupling constant of the grating waveguide is defined as Kand the Bragg wavelength thereof is defined as λ₀. In many DBR lasers,in many cases, with respect to the coupling constant K, the loss or gainin the grating waveguide can be ignored or an amount δβ≡2Πn (1/λ−1/λ₀)expressing a deviation of the oscillation wavelength λ of the DBR laserfrom the Bragg wavelength λ₀ can be ignored.

[0150] In these cases, a relations of ψ₁+ψ₂ to 2ψ₃ stands among theamounts ψ₁, ψ₂, and ψ₃ expressing phases of the reflectivity and thetransmittance.

[0151] Therefore, below, assuming that the relation of ψ₁+ψ₂=2ψ₃ stands,{circumflex over (Ø)} is defined as in the following equation in placeof the return light phase Ø.

{circumflex over (Ø)}≡Ø−ψ₂=Ø−2ψ₃−ψ₁   (36)

[0152] Then, it is understood that Y and Ŷ and Z and {circumflex over(Z)} are equal except the phase coefficient exp(iψ₁+iψ₄) over the entire{circumflex over (Z)}. Further, the forward optical output P_(f) dependsupon the absolute value |Z| of Z, but does not depend upon the phasethereof.

[0153] Accordingly, the maximum value ε* of the proportion of thefluctuation of the forward optical output P_(f) with respect to thechange of the return light phase Ø becomes the same as that of the caseof the FP laser already explained.

[0154] In the end, in many cases of a DBR laser as well, a semiconductorlaser in which the absolute value |ΔP_(f)| of the fluctuation of theforward optical output is a constant proportion ε or less with respectto the average optical output P_(av), that is, |ΔP_(f)|P_(av)≦ε*≦ε, canbe designed and fabricated by the same method as that of the case of anFP laser.

[0155] Note that the explanation was made by taking a semiconductorlaser as an example, but the present invention is not limited to asemiconductor laser and can be applied to other laser apparatuses.

[0156] Namely, when the injected current I is replaced by the excitationΔN⁰ and the threshold current value I_(th)+ΔI_(th) is replaced by thethreshold value ΔNth of the inverted distribution, the conclusion withrespect to the semiconductor laser that “the optical output can be heldconstant even if the return light phase changes” stands with respect toa general laser.

[0157] In this case, the rate equations regarding equations (10) and(11) can be discussed as follows.

[0158] Namely, the rate equations for describing the operation of thelaser are assumed as follows with respect to the number of photons Sinside the laser resonator and the number of atoms N₁ at a lower leveland the number of atoms N₂ at an upper level between two levels in alaser medium producing the inverted distribution due to the excitation.$\begin{matrix}{\frac{S}{t} = {{\frac{c}{n}\left\lbrack {{g_{N}\left( {N_{2} - N_{1}} \right)} - g} \right\rbrack}S}} & (37) \\{\frac{N_{2}}{t} = {\Phi_{2} - {\gamma_{2}N_{2}} - {{g_{N}\left( {N_{2} - N_{1}} \right)}S}}} & (38) \\{\frac{N_{1}}{t} = {\Phi_{1} - {\gamma_{1}N_{1}} + {{g_{N}\left( {N_{2} - N_{1}} \right)}S}}} & (39)\end{matrix}$

[0159] Here, it is assumed that the optical gain generated in the lasermedium due to excitation is proportional to the inverted distributionΔN≡N₂−N₁ and the proportional coefficient thereof was expressed byg_(N). Further, the contribution of the spontaneously emitted light withrespect to the change of the number of photons over time is notimportant, so is ignored in the following discussion. Further,excitations to respective levels are defined as Φ₁ and Φ₂ and relaxationconstants of levels are defined as γ₁and γ₂.

[0160] In the rate equations (37), (38), and (39), when finding S of thesteady oscillation state while setting S>0 and dS/dt=dN₂/dt=dN₁/dt=0,the following equation is obtained: $\begin{matrix}{S = {\frac{n}{2\quad {cg}\quad \tau}\left( {{\Delta \quad N^{0}} - {\Delta \quad N_{th}}} \right)}} & (40)\end{matrix}$

[0161] Here, ΔN_(th) indicates the threshold value of the inverteddistribution, ΔN⁰ indicates an amount expressing the intensity of theexcitation, and τ indicates the effective relaxation time of the laser.These are defined as follows: $\begin{matrix}{{\Delta \quad N_{th}} \equiv \frac{g}{g_{N}}} & (41) \\{{\Delta \quad N^{0}} \equiv {\frac{\Phi_{2}}{\gamma_{2}} - \frac{\Phi_{1}}{\gamma_{1}}}} & (42) \\{\tau \equiv {\frac{1}{2}\left( {\frac{1}{\gamma_{2}} + \frac{1}{\gamma_{1}}} \right)}} & (43)\end{matrix}$

[0162] Further, from S>0, equation (40) has meaning only when theexcitation ΔN⁰ is larger than the threshold value ΔN_(th), that is,ΔN⁰>ΔN_(th). In the case of ΔN⁰≦ΔN_(th), here, the contribution of thespontaneously emitted light is ignored, so S=0.

[0163] Further, equations (19) and (20) regarding the forward opticaloutput P_(f) and the slope efficiency η_(S) mentioned above areexpressed as in the following equations (44) and (45):

P _(f)=η_(S)(ΔN ⁰ −ΔN _(th))   (44)

[0164] $\begin{matrix}{\eta_{S} \equiv {\frac{\hslash\omega}{2\quad \tau}\frac{g - \alpha_{i}}{g}\frac{\left( {1 - R_{f}} \right)}{{Y}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}{Z}}} \right)\left( {1 + {\sqrt{R_{f}/R_{r}}{Z}}} \right)}}} & (45)\end{matrix}$

[0165] Then, equation (29) is expressed as follows: $\begin{matrix}{\varepsilon^{*} = \left. \frac{1}{2} \middle| \left\lbrack \left. {\frac{\eta_{S}(0)}{\eta_{S}^{0}} - \frac{\eta_{S}(\pi)}{\eta_{S}^{0}} + \quad {\frac{1}{P_{av}}{\frac{\eta_{S}^{0}}{g_{N}L_{in}}\left\lbrack {{\frac{\eta_{S}(0)}{\eta_{S}^{0}}\ln \quad {Z(0)}} - {\frac{\eta_{S}(\pi)}{\eta_{S}^{0}}\ln \quad {Z(\pi)}}} \right\rbrack}}} \right| \right. \right.} & (46)\end{matrix}$

[0166] Note that, in this case, the forward optical output P_(f) dependsupon the return light phase Ø=4ΠL_(ex)/λ through Y and Z contained inequations (41), (45), and (6) of ΔN_(th), η_(S), and g.

[0167] In this way, when reading the injected current I as theexcitation ΔN⁰ or the threshold current value I_(th)+ΔI_(th) as thethreshold value ΔN_(th) of the inverted distribution, the discussionwith respect to a semiconductor laser concluding that “the opticaloutput can be held constant even if the return light phase changes”stands with respect to a general laser as well.

[0168] As explained above, according to the present invention, there isthe advantage that the influence of the return light with respect to theoptical output can be suppressed without causing an increase of thenumber of parts, an enlargement of the entire apparatus, and an increaseof the power consumption.

[0169] While the invention has been described by reference to specificembodiments chosen for purposes of illustration, it should be apparentthat numerous modifications could be made thereto by those skilled inthe art without departing from the basic concept and scope of theinvention.

What is claimed is:
 1. A laser apparatus comprising an optical resonatorincluding a reflection portion and obtaining a constant optical outputfrom said optical resonator under constant drive conditions, wherein areflectivity of said reflection portion is set so as to absorb a changeof an output light intensity due to a change of a phase of a returnlight.
 2. A laser apparatus as set forth in claim 1, wherein the laserapparatus is a current-driven semiconductor laser and wherein thereflectivity of said reflection portion is set so that a predeterminedoptical output value exists in a region in which current-optical outputcharacteristics expressing the optical output with respect to the drivecurrent at different return light phases intersect.
 3. A laser apparatusas set forth in claim 2, wherein the optical resonator comprises aFabry-Perot resonator including the surface of the semiconductor or areflecting film on the surface of the semiconductor as a reflectionmirror.
 4. A laser apparatus as set forth in claim 2, wherein theoptical resonator comprises an optical resonator including a gratingwaveguide (DBR) built in the resonator as a reflection mirror.
 5. Alaser as set forth in claim 2, wherein the semiconductor laser is asurface emitting type laser having a vertical resonator as opticalresonator.
 6. A laser apparatus comprising an optical resonatorincluding a pair of opposing reflection mirrors, obtaining a constantoptical output from said optical resonator under constant driveconditions, and used built-in an optical system in which partR_(ofb)P(0<R_(ofb)<1) of the optical output P returns to the opticalresonator as return light, wherein when a time average value of theoptical output P is defined as P_(av), where an absolute value |ΔP| of afluctuation ΔP=P−P_(av) of the optical output produced along with thechange of a return light phase 0 must not be more than a constantproportion ε with respect to P_(av) and where |ΔP|/P_(av) must be notmore than ε, when the following are defined by designating areflectivity of the side (forward) for fetching the optical output ofthe pair of opposing reflection mirrors constituting said opticalresonator as R_(f), the reflectivity of the side opposite to this(reverse) as R_(r), a resonator length as L_(in), an internal loss asα_(i), a differential gain as g_(N), a proportion of coupling of thereturn light with the light inside the laser as η_(t), the proportion ofcoupling of the return light with the output light from the laser asη_(r), and an input/output efficiency and a threshold gain measured by alaser apparatus element where there is no return light as η_(S) ⁰ andg⁰, respectively, and using these parameters or physical constants:$Y_{1} = {1 + \sqrt{\eta_{r}R_{ofb}R_{f}}}$$Y_{2} = {1 - \sqrt{\eta_{r}R_{ofb}R_{f}}}$$Z_{1} = {1 + {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{1}}}}$$Z_{2} = {1 - {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{2}}}}$$g_{1} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{1}}}$$g_{2} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{2}}}$$\frac{\eta_{S1}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{1} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{1}\left( {g^{0} - \alpha_{i}} \right)}{Y_{1}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{1}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{1}}} \right)}$$\frac{\eta_{S2}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{2} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{2}\left( {g^{0} - \alpha_{i}} \right)}{Y_{2}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{2}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{2}}} \right)}$

the following stands:$\left. {{2\quad \varepsilon} \geq} \middle| {\left( {\frac{\eta_{S1}}{\eta_{S}^{0}} - \frac{\eta_{S2}}{\eta_{S}^{0}}} \right) + {\frac{\eta_{S}^{0}}{P_{av}g_{N}L_{in}\tau_{S}}\left\lbrack {{\frac{\eta_{S1}}{\eta_{S}^{0}}\ln \quad Z_{1}} - {\frac{\eta_{S2}}{\eta_{S}^{0}}\ln \quad Z_{2}}} \right\rbrack}} \right|$


7. A laser apparatus as set forth in claim 6, wherein the optical systemcomprises an optical disk recording or reproducing optical system.
 8. Asemiconductor laser as set forth in claim 6, wherein the optical systemcomprises an optical system coupled to an optical fiber.
 9. Asemiconductor laser apparatus comprising the optical resonator includinga pair of opposing reflection mirrors, obtaining a constant opticaloutput from said optical resonator under constant drive conditions, andused built-in an optical system in which part R_(ofb)P(0<R_(ofb)<1) ofthe optical output P returns to the optical resonator as return light,wherein when a time average value of the optical output P is defined asP_(av), where an absolute value |ΔP| of the fluctuation ΔP=P−P_(av) ofthe optical output produced along with a change of a return light phase0 must not be more than a constant proportion e with respect to P_(av)and where |ΔP|/P_(av) must be not more than a, when the following aredefined by designating a reflectivity of the side (forward) for fetchingthe optical output of the pair of opposing reflection mirrorsconstituting said optical resonator as R_(f), a reflectivity of the sideopposite to this (reverse) as R_(r), the resonator length as L_(in), theinternal loss as α_(i), a volume of an active region as V_(a), anoptical confinement coefficient of the active region as Γ, a proportionof an increase of the optical gain with respect to an increase of acarrier density of the active region as g_(N), a carrier life of thecarrier of the active region by spontaneous emission and a nonemissionrecoupling as τ_(s), a proportion of coupling of the return light withthe light inside the laser as η_(t), a proportion of coupling of thereturn light with an output light from the laser as η_(r), a slopeefficiency and the threshold gain measured by a laser apparatus elementwhere there is no return light as η_(S) ⁰ and g⁰, respectively, and anamount of charge as e, respectively, and using these parameters orphysical constants: $Y_{1} = {1 + \sqrt{\eta_{r}R_{ofb}R_{f}}}$$Y_{2} = {1 - \sqrt{\eta_{r}R_{ofb}R_{f}}}$$Z_{1} = {1 + {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{1}}}}$$Z_{2} = {1 - {\sqrt{\frac{\eta_{t}R_{ofb}}{R_{f}}}\frac{\left( {1 - R_{f}} \right)}{Y_{2}}}}$$g_{1} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{1}}}$$g_{2} = {g^{0} - {\frac{1}{L_{in}}\ln \quad Z_{2}}}$$\frac{\eta_{S1}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{1} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{1}\left( {g^{0} - \alpha_{i}} \right)}{Y_{1}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{1}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{1}}} \right)}$$\frac{\eta_{S2}}{\eta_{S}^{0}} = \frac{{g^{0}\left( {g_{2} - \alpha_{i}} \right)}\left( {1 - \sqrt{R_{f}R_{r}}} \right)\left( {1 + \sqrt{R_{f}/R_{r}}} \right)}{{g_{2}\left( {g^{0} - \alpha_{i}} \right)}{Y_{2}^{2}\left( {1 - {\sqrt{R_{f}R_{r}}Z_{2}}} \right)}\left( {1 + {\sqrt{R_{f}/R_{r}}Z_{2}}} \right)}$

the following stands:$\left. {{2\quad \varepsilon} \geq} \middle| {\left( {\frac{\eta_{S1}}{\eta_{S}^{0}} - \frac{\eta_{S2}}{\eta_{S}^{0}}} \right) + {\frac{{eVa}\quad \eta_{S}^{0}}{P_{av}{\Gamma g}_{N}L_{in}\tau_{S}}\left\lbrack {{\frac{\eta_{S1}}{\eta_{S}^{0}}\ln \quad Z_{1}} - {\frac{\eta_{S2}}{\eta_{S}^{0}}\ln \quad Z_{2}}} \right\rbrack}} \right|$


10. A semiconductor laser as set forth in claim 9, wherein the opticalresonator comprises a Fabry-Perot resonator including the surface of thesemiconductor or a reflecting film on the surface of the semiconductoras a reflection mirror.
 11. A semiconductor laser as set forth in claim9, wherein the optical resonator comprises an optical resonatorincluding a grating waveguide (DBR) built In the resonator as areflection mirror.
 12. A semiconductor laser as set forth in claim 9,wherein the semiconductor laser comprises a surface emitting type laserhaving a vertical resonator as optical resonator.
 13. A semiconductorlaser as set forth in claim 9, wherein the optical system comprises anoptical disk recording or reproducing optical system.
 14. Asemiconductor laser as set forth in claim 9, wherein the optical systemcomprises an optical system coupled to an optical fiber.